Difference between revisions of "ApCoCoA-1:Bertini.BMSolve"

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<description>
 
<description>
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
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This function solves a polynomial system of equations using multihomogeneous homotopy. The system of polynomials must be square. If the system has N variables then multihomogeneous homotopy will introduce N homogeneous variables to solve the system.
 
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<item>@param <em>P</em>: List of polynomials of the given system.</item>
 
<item>@param <em>P</em>: List of polynomials of the given system.</item>

Revision as of 10:22, 12 May 2010

Bertini.BMSolve

Solves a zero dimensional non-homogeneous polynomial system using multi-homogenization and default configurations.

Syntax

Bertini.BMSolve(P:LIST):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

This function solves a polynomial system of equations using multihomogeneous homotopy. The system of polynomials must be square. If the system has N variables then multihomogeneous homotopy will introduce N homogeneous variables to solve the system.

  • @param P: List of polynomials of the given system.

  • @return A list of lists containing the finite solutions of the polynomial system P.

Example

-- We want to solve the non-homogenous polynomial system x[1]^2+x[2]^2-5=0, x[1]x[2]-2=0, using multi-homogenization. 

Use S ::= QQ[x[1..2]];             
P := [x[1]^2+x[2]^2-5, x[1]x[2]-2];

-- Then we compute the solution with
Bertini.BMSolve(P);

-- And we achieve a list of lists containing finite solutions.
----------------------------------------
[[Vector(1000000000000001/1000000000000000, -2305082859180703/100000000000000000000000000000),
 Vector(1999999999999971/1000000000000000, 4135565953005217/100000000000000000000000000000)],
 [Vector(1000000000000003/500000000000000, 2604577577014449/50000000000000000000000000000),
 Vector(500000000000001/500000000000000, -619892334722183/25000000000000000000000000000)],
 [Vector(-2, 1724810333092189/1000000000000000000000000000000),
 Vector(-500000000000001/500000000000000, -355984244774691/200000000000000000000000000000)],
 [Vector(-9999999999999971/10000000000000000, -4053926086793577/1000000000000000000000000000000),
 Vector(-1999999999999999/1000000000000000, -3669041992638223/5000000000000000000000000000000)]]
--For Bertini output files refer to ApCoCoA directory/Bertini.
------------------------------------------




See also

Bertini.BCMSolve

Bertini.BSolve

Bertini.BUHSolve



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